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Inlii_indjoint.m
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Inlii_indjoint.m
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function Inli = Inlii(A, Pjoint)
% calculate redundancy from negative local interaction information
% A - cell array of elements
% Pjoint - full joint distribution
s = size(Pjoint);
Sm = s(end); % number of target values
Nx = length(s)-1; % number of dependent variables
vars = 1:Nx;
NA = length(A);
if NA>3
error('Inli: only 3 elements supported')
end
Pele(NA).Pa = []; % intialize struct
Am = zeros(1,NA); % number of symbols in each element
% Ps
Ps = Pjoint;
for xi=1:Nx
Ps = squeeze(sum(Ps,1));
end
% sort elements
A = cellfun(@sort, A, 'Unif',false);
% build distributions for each element
for ai=1:NA
thsA = A{ai};
Nv = length(thsA);
% vars to sum over
sumover = setdiff(vars, thsA);
Pas = Pjoint;
for ii=1:length(sumover)
Pas = sum(Pas, sumover(ii));
end
% joint distribution P(a,s)
Pas = squeeze(Pas);
% target first axis to collapse over non-target axes
% Pas = permute(Pas, [Nv+1 1:Nv]);
% Pas = Pas(:,:)';
s = size(Pas);
Pas = reshape(Pas, [prod(s(1:end-1)) s(end)]);
Pele(ai).Pas = Pas;
% unconditional distribution P(a)
Pele(ai).Pa = squeeze(sum(Pas,2));
Pele(ai).Pacs = bsxfun(@rdivide, Pele(ai).Pas, Ps);
Am(ai) = size(Pas,1);
end
% build pairwise joint element distributions
if NA>1
pairs = nchoosek(1:NA,2);
Npair = size(pairs,1);
Ppair(Npair).Paa = []; % intialize struct
for pi=1:Npair
p1 = pairs(pi,1);
p2 = pairs(pi,2);
Ppair(pi).Paacs = zeros(Am(p1),Am(p2),Sm);
for si=1:Sm
Paacs(:,:,si) = Pele(p1).Pacs(:,si) * Pele(p2).Pacs(:,si)';
end
Ppair(pi).Paacs = Paacs;
Paas = bsxfun(@times, Paacs, reshape(Ps,[1 1 Sm]));
Ppair(pi).Paas = Paas;
Ppair(pi).Paa = nansum(Paas,3);
end
end
% build triplewise joint element distributions
Paaas = cell(1,NA);
if NA==3
Paaacs = zeros(Am(1),Am(2),Am(3),Sm);
for si=1:Sm
for a3=1:Am(3)
for a2=1:Am(2)
for a1=1:Am(1)
Paaacs(a1,a2,a3,si) = Pele(1).Pacs(a1,si) * Pele(2).Pacs(a2,si) * Pele(3).Pacs(a3,si);
end
end
end
end
Ptrip(1).Paaacs = Paaacs;
Paaas = bsxfun(@times, Paaacs, reshape(Ps,[1 1 1 Sm]));
Ptrip(1).Paaas = Paaas;
Ptrip(1).Paaa = nansum(Paaas,4);
end
% pointwise interaction information
pii = zeros([Am Sm]);
if NA==1
for a1=1:Am(1)
for si=1:Sm
% local interaction information
% = neg local mutual information
num = Pele(1).Pa(a1) * Ps(si);
den = Pele(1).Pas(a1,si);
if den==0
ii = 0;
else
ii = log2(num ./ den);
end
pii(a1,si) = ii;
end
end
pii = Pele(1).Pas .* pii;
elseif NA==2
for a1=1:Am(1)
for a2=1:Am(2)
for si=1:Sm
num = Pele(1).Pa(a1) * Pele(2).Pa(a2) * Ps(si) * Ppair(1).Paas(a1,a2,si);
den = Pele(1).Pas(a1,si) * Pele(2).Pas(a2,si) * Ppair(1).Paa(a1,a2);
ii12 = log2(num ./ den);
% if num>0
% dsj = log2( Ppair(1).Paas(a1,a2,si) / (Ppair(1).Paa(a1,a2)*Ps(si)) );
% ds1 = log2( Pele(1).Pas(a1,si) ./ (Pele(1).Pa(a1)*Ps(si)) );
% ds2 = log2( Pele(2).Pas(a2,si) ./ (Pele(2).Pa(a2)*Ps(si)) );
% keyboard
% end
num = Pele(1).Pa(a1) * Ps(si);
den = Pele(1).Pas(a1,si);
if den==0
ii1 = 0;
else
ii1 = log2(num ./ den);
end
num = Pele(2).Pa(a2) * Ps(si);
den = Pele(2).Pas(a2,si);
if den==0
ii2 = 0;
else
ii2 = log2(num ./ den);
end
% pii(a1,a2,si) = nanmax([ii12 ii1 ii2]);
pii(a1,a2,si) = ii12;
end
end
end
pii = Ppair(1).Paas .* pii;
elseif NA==3
for a1=1:Am(1)
for a2=1:Am(2)
for a3=1:Am(3)
for si=1:Sm
num = Pele(1).Pa(a1) * Pele(2).Pa(a2) * Pele(3).Pa(a3) * Ps(si);
num = num * Ppair(1).Paas(a1,a2,si) * Ppair(2).Paas(a1,a3,si) * Ppair(3).Paas(a2,a3,si);
num = num * Ptrip(1).Paaa(a1,a2,a3);
den = Pele(1).Pas(a1,si) * Pele(2).Pas(a2,si) * Pele(3).Pas(a3,si);
den = den * Ppair(1).Paa(a1,a2) * Ppair(2).Paa(a1,a3) * Ppair(3).Paa(a2,a3);
den = den * Ptrip(1).Paaas(a1,a2,a3,si);
ii123 = log2(num ./ den);
% pair(1) = 1 2
num = Pele(1).Pa(a1) * Pele(2).Pa(a2) * Ps(si) * Ppair(1).Paas(a1,a2,si);
den = Pele(1).Pas(a1,si) * Pele(2).Pas(a2,si) * Ppair(1).Paa(a1,a2);
ii12 = log2(num ./ den);
% pair(2) = 1 3
num = Pele(1).Pa(a1) * Pele(3).Pa(a3) * Ps(si) * Ppair(2).Paas(a1,a3,si);
den = Pele(1).Pas(a1,si) * Pele(3).Pas(a3,si) * Ppair(2).Paa(a1,a3);
ii13 = log2(num ./ den);
% pair(3) = 2 3
num = Pele(2).Pa(a2) * Pele(3).Pa(a3) * Ps(si) * Ppair(3).Paas(a2,a3,si);
den = Pele(2).Pas(a2,si) * Pele(3).Pas(a3,si) * Ppair(3).Paa(a2,a3);
ii23 = log2(num ./ den);
num = Pele(1).Pa(a1) * Ps(si);
den = Pele(1).Pas(a1,si);
if den==0
ii1 = 0;
else
ii1 = log2(num ./ den);
end
num = Pele(2).Pa(a2) * Ps(si);
den = Pele(2).Pas(a2,si);
if den==0
ii2 = 0;
else
ii2 = log2(num ./ den);
end
num = Pele(3).Pa(a3) * Ps(si);
den = Pele(3).Pas(a3,si);
if den==0
ii3 = 0;
else
ii3 = log2(num ./ den);
end
% pii(a1,a2,a3,si) = nanmax([ii123 ii12 ii13 ii23 ii1 ii2 ii3]);
% max over sub-pairs enforces monoticity
% pii(a1,a2,a3,si) = nanmax([ii123 ii12 ii13 ii23]);
% direct interaction information (not monotonic)
pii(a1,a2,a3,si) = ii123;
% if nansum(nanmax([ii123 ii12 ii13 ii23])) ~= nansum(nanmax(ii123)) && Ptrip(1).Paaas(a1,a2,a3,si)~=0
% keyboard
% end
end
end
end
end
pii = Ptrip(1).Paaas .* pii;
end
% pii(~isfinite(pii))=0;
% pii
locred = -nansum(pii(pii<0));
Inli = locred;
function Pnew = copy_var(P, var, newpos)
% form joint distribution with variable var copied to axis position newpos
s = size(P);
varM = s(var);
% size of new array
news = [s(1:newpos-1) varM s(newpos:end)];
Pnew = zeros(news);
subP = cell(1,ndims(P));
[subP{:}] = ind2sub(size(P),1:numel(P));
subPnew = [subP(1:newpos-1) subP(var) subP(newpos:end)];
indPnew = sub2ind(size(Pnew), subPnew{:});
Pnew(indPnew) = P(:);